Question
Download Solution PDFIf a circle whose centre is (2, 3) touches the line 4x + 3y - 7 = 0, then the radius of the circle is:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Center of the circle = (2, 3)
Equation of the line = 4x + 3y - 7 = 0
Formula used:
Distance from a point (x₁, y₁) to a line ax + by + c = 0 is:
Distance = |a x₁ + b y₁ + c| / √(a² + b²)
Calculations:
Substitute (x₁, y₁) = (2, 3) and the line equation 4x + 3y - 7 = 0 into the formula:
Distance = |(4 × 2) + (3 × 3) - 7| / √(4² + 3²)
⇒ Distance = |8 + 9 - 7| / √(16 + 9)
⇒ Distance = |10| / √25
⇒ Distance = 10 / 5
⇒ Distance = 2
∴ The radius of the circle is 2 units.
Last updated on May 28, 2025
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